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Unformatted text preview: Hypothesis Hypothesis Testing Testing Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. H. G. Wells Learning Objectives Understand the normal distribution and standard normal distribution. Understand what a sampling distribution is. Understand the nature and logic of hypothesis testing. Understand what a statistically significant difference is. Understand how to do hypotheses testing using SPSS. Normal Distribution First discovered by de Moivre (16671754) in1733 Rediscovered by Laplace (17491827) and also by Gauss (17771855) in their studies of errors in astronomical measurements. Often referred to as the Gaussian distribution. Normal (Gaussian) Distribution Continuous, symmetric, bellshaped curve. Determined by two parameters, these being arithmetic mean and standard deviation , N(, ) . Area under curve represents probability. 100 IQ < < = x e x f x for 2 1 ) ( ) 2 /( ) ( 2 2 Normal (Gaussian) Distribution Standard Normal Distribution Also referred to as the Z distribution. Definition: Z = (X )/ (Standardizing). When X is normally distributed, Z is N(0, 1). Standardization allows distributions to be compared on a single scale. Normal Tables and ZValues Find the probability that a standard normal random variable is less than 1.35. Locate 1.3 along the left and 0.05 along the top, and then read into the table to find the probability 0.91149. The probability is about 0.91 that a standard normal random variable is less than 1.35. Find the probability that a standard normal random variable is less than 0.55. Find the probability that a standard normal random variable is between 0.55 and 1.35. Normal Tables and ZValues Find the standardized value corresponding to a probability of 0.75. Locate the probability in the table that is closest to 0.75, and then reading to the left and up. With interpolation, the required value is about 0.675. Thus, the probability of being to the left of 0.675 under the standard normal curve is approximately 0.75. Find the standardized value corresponding to a probability of 0.55. Normal Tables and ZValues Suppose X (IQ of people in HK) is normally distributed with mean 100 and standard deviation 10. Find the probability that the IQ of a randomly selected individual is less than 115. 0.93319. y probabilit the obtain to column) .00 row, (1.5 table the up Look 5 . 1 10 100 115 X Z Compute = = = Find the 85 th percentile of the above standard normal distribution. How many Einsteins are there in HK (IQ > 160)?...
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 Fall '08
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